A function of automatically threading a wire electrode has been implemented. In particular, a curve of a wire electrode due to the electrode having been wound on a wire bobbin is straitened, such that the wire electrode is automatically threaded even through a thick workpiece of 100 mm or more if an initial hole has already been formed in the workpiece, thereby enabling a start of electrical discharge machining. In this case, however, since it is necessary to perform machining of the initial hole in the workpiece in advance, the workpiece should be placed on a wire electrical discharge machine after the initial hole is machined in the workpiece by a dedicated machine, or a dedicated unit for the initial hole machining should be mounted on the wire electrical discharge machine. Both of these two approaches require a re-setup, and thus fully automatic initial-hole machining has not been implemented.